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Proof step 31 from proof inv-write_inode (previous step)

files[ino] = mkfile(m0, md2, m1, content0), files[m] = mkfile(m3, md0, # links(m, dirs), content), dirs[m] = mkdir(m5, md1, m6, m7, entries), afs-cons(dirs, files), m ∈ files, ROOT_INO ∈ dirs, ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅, ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files ⊦ ( ino ∈ files → ¬ ino ∈ dirs ∧ (ino = m ⊃ mkfile(m2, md, # links(m, dirs), content);mkfile(m0, md2, m1, content0)).nlink = # links(ino, dirs)) ∧ ( ino ∈ files ∧ n ∈ (ino = m ⊃ mkfile(m2, md, # links(m, dirs), content);mkfile(m0, md2, m1, content0)).content → # (ino = m ⊃ mkfile(m2, md, # links(m, dirs), content);mkfile(m0, md2, m1, content0)).content[n] = VFS_PAGE_SIZE)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
(ino = m ⊃ mkfile(m2, md, # links(m, dirs), content);mkfile(m0, md2, m1, content0)) = mkfile(m4, md3, m8, content1), dirs[m] = mkdir(m5, md1, m6, m7, entries), files[m] = mkfile(m3, md0, # links(m, dirs), content), files[ino] = mkfile(m0, md2, m1, content0), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ files, ino ∈ dirs ∧ name ∈ dirs[ino].entries → dirs[ino].entries[name] ∈ dirs ∨ dirs[ino].entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs ∧ m1 = # links(ino, dirs), ino ∈ dirs → dirs[ino].nlink = # links(ino, dirs) ∧ dirs[ino].nlink ≤ 1 ∧ dirs[ino].size = # dirs[ino].entries ∧ dirs[ino].nsubdirs = # subdirs(ino, dirs), ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → dirs[ino].entries = ∅ ⊦ (ino ∈ files → ¬ ino ∈ dirs ∧ m8 = # links(ino, dirs)) ∧ (ino ∈ files ∧ n ∈ content1 → # content1[n] = VFS_PAGE_SIZE)

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [(ino = m ⊃ mkfile(m2, md, # links(m, dirs), content) ;mkfile(m0, md2, m1, content0) ), m4, md3, m8, content1]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: (ino = m ⊃ mkfile(m2, md, # links(m, dirs), content) ;mkfile(m0, md2, m1, content0) ), m4, md3, m8, content1